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A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…
P\'olya trees are rooted, unlabeled trees on $n$ vertices. This paper gives an efficient, new way to generate P\'olya trees. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with…
Discrete normal distributions are defined as the distributions with prescribed means and covariance matrices which maximize entropy on the integer lattice support. The set of discrete normal distributions form an exponential family with…
Random flights in $\mathbb{R}^d,d\geq 2,$ with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position $\underline{\bf X}_d(t),\,t>0,$ when the number of…
We introduce two non-homogeneous processes: a fractional non-homogeneous Poisson process of order $k$ and and a fractional non-homogeneous P\'olya-Aeppli process of order $k$. We characterize these processes by deriving their non-local…
In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…
Information-theoretic measures such as the entropy, cross-entropy and the Kullback-Leibler divergence between two mixture models is a core primitive in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
Given a general critical or sub-critical branching mechanism and its associated L\'evy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the…
In this paper, we describe a Bayesian nonparametric approach to make inference for a bivariate spherically symmetric distribution. We consider a Dirichlet invariant process prior on the set of all bivariate spherically symmetric…
We compute probability distributions of trajectory observables for reversible and irreversible growth processes. These results reveal a correspondence between reversible and irreversible processes, at particular points in parameter space,…
Bayesian Additive Regression Trees (BART) is a fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high dimensional regressors in a fairly automatic way and provide Bayesian…
In this article we study the influence of regularly varying probability measures on additive and multiplicative Boolean convolutions. We introduce the notion of Boolean subexponentiality (for additive Boolean convolution), which extends the…
The P\'olya urn scheme is a discrete-time process concerning the addition and removal of colored balls. There is a known embedding of it in continuous-time, called the P\'olya process. We deal with a generalization of this stochastic model,…
In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…
Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with…
The purpose of this note is to collect in one place a few results about simple random walk and Brownian motion which are often useful. These include standard results such as Beurling estimates, large deviation estimates, and a method for…
The analysis of continuously spatially varying processes usually considers two sources of variation, namely, the large-scale variation collected by the trend of the process, and the small-scale variation. Parametric trend models on latitude…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…